2 Conjugate Variables and Einstein’s Law
of Special Relativity
Since our efforts concern both material and immaterial organisations, examined at
the very limit of physical theory, our formulation starts at the microscopic level of
atomic and molecular constituents in the grey zone between quantum and classical
readings. It is important to understand that we do not refer to popular developments
in terms of exotic dimensions at unconventional scales, as we do believe that a
solution of the problems indicated above does not originate in any of the popular
superstring theories, Green et al. [3].
Many physicists today are undeniably epistemologists. However, brane and
string scientist seem to have a different ontology in that they consider the vibrating
string to be the particle itself rather than merely dictating the properties of its host
particle. This view may not be commensurate with a quantum theoretic hierarchy of
concepts, i.e. representing nature via accumulation of knowledge through unbiased
and systematic research. Indeed the absolute being of material bodies, obtains selfreferential consequences, provoking further discussions in relation to Gödel’s
incompleteness theorem(s) [4]. In short Gödel’s self-referential account will be the
guide for teleonomic processes, already emerging on the molecular level, introducing viable communication protocols via Poisson distributed channels, for details
see more below. In contrast modern p-branes, while being spatially extended
strings, originate in mathematical concepts that appear to conflate matter with its
mathematical description, i.e. do not exhibit the proper fabric for a self-referential
examination. We will here advance an ontology that entangles the physical- and the
mental world, while embedding evolution as a template for self-organization and
associated teleodynamical processes.
It is then most natural to begin the formulation by quoting Kant: Space and Time
are the two essential forms of human sensibility. Once space and time are mathematically well defined their conjugate variables follow naturally, i.e. as originally
expressed by Einstein, via the energy, represented as E op below, and momentum,
~ p op , combined in the four-momentum or the energy- momentum tensor. The conjugate variables of energy–momentum, time and space are further characterized as
s ¼ T op and ~ x op below, with h being Planck’s constant divided by 2π, and ~
r being
the nabla operator. Thus we have the following four key operators for our general
exposition
E op ¼ i h
@
@t
; ~ p op ¼ Ài hr
!
~ x
ð2:1Þ
s ¼ T op ¼ Ài h
@
@E
; ~ x op ¼ i hr
!
~ p
ð2:2Þ
The operators above do not out of context define any proper physical realizations
as their relevance is acquired from the insertion of appropriate boundary conditions
250
E.J. Brändas
of Special Relativity
Since our efforts concern both material and immaterial organisations, examined at
the very limit of physical theory, our formulation starts at the microscopic level of
atomic and molecular constituents in the grey zone between quantum and classical
readings. It is important to understand that we do not refer to popular developments
in terms of exotic dimensions at unconventional scales, as we do believe that a
solution of the problems indicated above does not originate in any of the popular
superstring theories, Green et al. [3].
Many physicists today are undeniably epistemologists. However, brane and
string scientist seem to have a different ontology in that they consider the vibrating
string to be the particle itself rather than merely dictating the properties of its host
particle. This view may not be commensurate with a quantum theoretic hierarchy of
concepts, i.e. representing nature via accumulation of knowledge through unbiased
and systematic research. Indeed the absolute being of material bodies, obtains selfreferential consequences, provoking further discussions in relation to Gödel’s
incompleteness theorem(s) [4]. In short Gödel’s self-referential account will be the
guide for teleonomic processes, already emerging on the molecular level, introducing viable communication protocols via Poisson distributed channels, for details
see more below. In contrast modern p-branes, while being spatially extended
strings, originate in mathematical concepts that appear to conflate matter with its
mathematical description, i.e. do not exhibit the proper fabric for a self-referential
examination. We will here advance an ontology that entangles the physical- and the
mental world, while embedding evolution as a template for self-organization and
associated teleodynamical processes.
It is then most natural to begin the formulation by quoting Kant: Space and Time
are the two essential forms of human sensibility. Once space and time are mathematically well defined their conjugate variables follow naturally, i.e. as originally
expressed by Einstein, via the energy, represented as E op below, and momentum,
~ p op , combined in the four-momentum or the energy- momentum tensor. The conjugate variables of energy–momentum, time and space are further characterized as
s ¼ T op and ~ x op below, with h being Planck’s constant divided by 2π, and ~
r being
the nabla operator. Thus we have the following four key operators for our general
exposition
E op ¼ i h
@
@t
; ~ p op ¼ Ài hr
!
~ x
ð2:1Þ
s ¼ T op ¼ Ài h
@
@E
; ~ x op ¼ i hr
!
~ p
ð2:2Þ
The operators above do not out of context define any proper physical realizations
as their relevance is acquired from the insertion of appropriate boundary conditions
250
E.J. Brändas